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3 years ago

Y=3x+14 2x-3y=-14 Substitution method

Mathematics

2 answers:

riadik2000 [5.3K]3 years ago

5 0

X=-8

I know it’s that so it’s does not need a explanation

Montano1993 [528]3 years ago

4 0

Answer:

x = -8

Step-by-step explanation:

y = 3x + 14

2x - 3y = -14

So, what is the substitution? Y of course, this is because y is equal to 3x + 14.

2x - 3 (3x + 14) = -14

Multiply 3 with the numbers in the parentheses.

2x - 9x + 42 = -14

So you maybe be wondering why it is a negative 7 instead of subtracting 9 with 2. Using PEMDAS, we always read from left to right. So it is basically 2 -9 and you get -7.

-7x + 42 = -14

Then subtract 42 from both sides.

-7x + 42 - 42 = -14 - 42

Simplify

-7x = -56

Divide 7 by both sides.

-7x / 7 = -56 / 7

x = -8

And you might ask, why we get x instead afterwards. This is because both -7 and 7 cancel each other out leaving us with x.

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A hiker is hiking in a valley. The height of the valley is h(x,y)=4x2+y2 where x and y are the east-west and north-south distanc

Ainat [17]

Answer:

A. $\frac{\partial{h}}{\partial{t}}=0$

Step-by-step explanation:

A. The problems asked for 2 ways to solve it, expanding the equation with the substitution x(t)=2 cos(t) and y(t)=4 sin(t) to differentiate it . The other way is by chain rule.

Expanding and differentiating:

We start by substituting x(t)=2 cos(t) and y(t)=4 sin(t) in h(x,y)=4x2+y2:

$h(x,y)=4x^{2}+y^{2}= 4(2cos(t))^{2}+(4sin(t))^{2}\\h(x,y)=4(4cos^{2}(t))+(16sen^{2}(t))\\h(x,y)=16cos^{2}(t)+16sen^{2}(t)=16(sen^{2}(t)+cos^{2}(t))\\h(x,y)=16$

So, in the path that the hiker chose:

$\frac{\partial{h}}{\partial{t}}=0$

Chain rule:

We start differentiating h(x,y) using chain rule as follows:

$\frac{\partial{h}}{\partial{t}}= \frac{\partial{h}}{\partial{x}}\frac{\partial{x}}{\partial{t}}+\frac{\partial{h}}{\partial{y}}\frac{\partial{y}}{\partial{t}}$

Now, it´s easy to find all these derivatives:

$\frac{\partial{h}}{\partial{x}}=8x\\\frac{\partial{x}}{\partial{t}}=-2sin(t)\\\frac{\partial{h}}{\partial{y}}=2y\\\frac{\partial{y}}{\partial{t}}=4cos(t)$

Now we replace them in the chain rule, with the replacement x=2cos(t) and y=4sin(t) in the x,y that are left and we operate everything:

$\frac{\partial{h}}{\partial{t}}= 8x(-2sin(t))+2y(4cos(t)$

$\frac{\partial{h}}{\partial{t}}= 8(2cos(t))(-2sin(t))+2(4sin(t))(4cos(t)$

$\frac{\partial{h}}{\partial{t}}= -32cos(t)sin(t)+32sin(t)cos(t)$

$\frac{\partial{h}}{\partial{t}}= 0$

This will be our answer

6 0

3 years ago

HELP DUE SOON EMERGENCY

algol [13]

Answer:

The sum of the series is 44.

Step-by-step explanation:

Sigma notation. I just had a test on this, so this is pretty good timing.

Below the sigma, we see that k = 1. This means that 1 is the number you would substitute for k into the expression on the right to get the first term. In this case, the first term is -2. (2(1)² - 4)

Now, we can also find out the number of terms in the series by subtracting 1 (taken from k = 1) from the number on top of the sigma, 4, and then adding 1 to it.

4 - 1 + 1 = 4. This means there are 4 terms in the series.

See the remaining work in the attached file. You should get that the sum of the series is 44.

Hope this helps!